Message #1413

From: Eduard <>
Subject: Re: The 3 slice pentachoron
Date: Tue, 15 Feb 2011 20:59:21 -0000

Thanks for the answer.

— In, "Matthew" <damienturtle@…> wrote:
> With a little thought, the {3,3,3}3 puzzle (this can serve to check I’m thinking of the correct puzzle) is fairly easy to solve. The octahedra located around a vertex are one piece and can easily be orientated correctly, and the tetrahedra at each vertex are equivalent to the trivial tips on a pyraminx and thus are easy to solve in a similar manner, although you know all this already. This leaves the 10 edges which can be 3-cycled using basically the same 4-move sequence which applies on a normal pyraminx. This allows the sequence which flips 2 edges on a pyraminx to also apply. A slight change in 4D is similar to one found on the 3x3x3x3: you can have a single edge with incorrect orientation. Think about the previous sequence to flip 2 edges in place (switching 2 stickers on each, to clarify). Perform this, then perform a single twist about an edge to change the stickers being swapped on one of those edges. Then repeat (or undo) the flipping sequence and undo the edge twist. I will upload a log file demonstrating this after posting. Any more questions, just ask (I sometimes don’t explain things well).
> Matt
> PS. Funny coincidence, my Meffert’s Professor Pyraminx arrived today, so I might do the {3,3,3}5 for fun sometime soon. When/if I do, I can write a short guide if there is enough interest, although I feel that most of the fun in this group is covering new ground and solving puzzles with no tutorial to follow.
> — In, "Eduard" <baumann@> wrote:
> >
> >
> > I asked in this forum for instructions for the pentachoron (3 slices).
> >
> > Since I got no reaction I think that these instructions do not exist. At
> > least not for a layered solution (as Roice’s for the magic cube). This
> > is not astonishing because the pentachoron beeing smaller (only 5 cells
> > compared with the 8 cells of the magic cube) seems to be more ensnared.
> > Reading (watching, playing) the log files from R.Durka I can’t learn
> > anything. Does he use computer aid?
> >
> > We can distinguish the following technics (1) fully by hand, (2) by hand
> > and macros, (3) with heavy computer aid. I’m doing (2).
> >
> > Without any macros and commutators you can do the 5 faces with 4
> > differently colored octahedra. Then the 5 fourcolored corners can be
> > done with slice 3 twists only.
> > After that you have the hard core of the job to be done: the 10
> > threecolored edges. For the moment I have established a 3-cycles across
> > an edge, a 3-cycle in a face and a 3-cycle around a vertex. I have also
> > a concept for a sequence which mirrors two edges in their place. I need
> > also a sequence to turn two edges in their place. All these sequences
> > work with slice 2 twists of course.
> >